Computer simulation study of a two-dimensional nematogenic lattice model based on the Nehring–Saupe interaction potential

Abstract

We have considered a nematogenic lattice model, consisting of 3-component unit vectors, associated with a 2-dimensional lattice, and interacting via the nearest-neighbour potential model proposed by Nehring and Saupe [Int. J. Mod. Phys. 54 (1971) 337], and already studied by simulation in 3 dimensions [Int. J. Mod. Phys. 13 (1999) 3879; Mod. Phys. Lett. B 15 (2001) 137]. The model is defined by Ψ jk=ϵ − 3 2 (3a ja k−τ jk) 2+1 , r = x j− x k, s = r /| r |, a j= u j· s , a k= u k· s , τ jk= u j· u k. Here the 2-component vectors x j∈Z 2 define centre-of-mass coordinates of the particles, and u k are three-component unit vectors defining their orientations; ϵ is a positive quantity setting energy and temperature scales (i.e., T ∗=k B T/ϵ ); this model can be regarded as the anisotropic counterpart to the generic Lebwohl–Lasher lattice model; in 2 dimensions, its anisotropic character does not preclude the existence of orientational order at finite temperature. The model produces a ground state where particles are aligned along a lattice axis; both Mean Field (MF) predictions and simulation results for the second-rank ordering tensor show a low-temperature regime where the system becomes biaxial, with the main director aligned along a lattice axis; at higher temperature there is a transition to uniaxial order with negative order parameter, and director orthogonal to the lattice plane; this orientational order survives up to temperatures higher than the transition temperature of the 3-dimensional counterpart, possibly at all finite temperatures. MF predictions and simulation results appear to agree qualitatively, but in quantitative terms the MF prediction for the transition temperature is some 45% too high.